Stochastic control applications and higher-order approximation of strongly coupled Forward-Backward Stochastic Differential Equations

强耦合前向-后向随机微分方程的随机控制应用和高阶近似

• 批准号: 299077261
• 负责人: Professor Dr. Stefan Ankirchner
• 金额: --
• 依托单位: Lehrstuhl für Stochastische Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/299077261?language=en
• 关键词: Stochastic; control; applications; higher; order

The project deals with Forward-Backward Stochastic Differential Equations (FBSDEs). In the first part of the project we will analyze a particular class of stochastic control problem, referred to as target problem, that consists in minimizing a cost functional over a class of absolutely continuous paths vanishing at a given terminal time. By applying the stochastic maximum principle one can reduce the problem to a FBSDE. The project's first main aim is to understand to which extent one can solve the associated FBSDEs, and hence the original target problems. We plan to advance a new method, called method of decoupling fields, for showing whether a strongly coupled FBSDEs possesses a solution or not. We will hereby strive to keep the objective functional of the stochastic control problem as general as possible.The project's second objective is to develop algorithms that allow to compute higher-order approximations of strongly coupled FBSDEs. To this end we will draw on Ito-Taylor-expansions of the systems. We will set up an algorithm estimating the coefficients of the Ito-Taylor-expansion implicitly by minimizing a suitable error functional. The goal is to prove the convergence properties of such enhanced algorithms.

该项目涉及向前向后随机微分方程（FBSDES）。在项目的第一部分中，我们将分析一类特殊的随机控制问题，称为目标问题，它包括在最小化一类绝对连续路径在给定的终端时间消失的成本泛函。通过应用随机最大值原理，人们可以将问题简化为一个FBBNN。该项目的第一个主要目标是了解在何种程度上可以解决相关的FBSDE，因此，原来的目标问题。 我们计划提出一种新的方法，称之为解耦场方法，以显示是否有一个强耦合的FBSDES有解或没有。因此，我们将努力保持目标功能的随机控制问题尽可能一般。该项目的第二个目标是开发算法，允许计算高阶近似的强耦合FBSDES。为此，我们将利用系统的伊藤-泰勒展开式。我们将建立一个算法估计系数的伊藤-泰勒展开隐式最小化一个合适的误差泛函。我们的目标是证明这种增强算法的收敛性。

项目成果

A transformation method to study the solvability of fully coupled FBSDEs

研究全耦合 FBSDE 可解性的变换方法

• DOI: 10.1080/17442508.2021.1903466
• 发表时间: 2022
• 期刊: Stochastics
• 影响因子: 0.9
• 作者: Stefan Ankirchner;Alexander Fromm;Julian Wendt
• 通讯作者: Julian Wendt

The Skorokhod embedding problem for inhomogeneous diffusions

非均匀扩散的 Skorokhod 嵌入问题

• DOI: 10.1214/19-aihp1012
• 发表时间: 2020
• 期刊: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
• 作者: Stefan Ankirchner;Stefan Engelhardt;Alexander Fromm;Gonçalo dos Reis
• 通讯作者: Gonçalo dos Reis

Optimal position targeting via decoupling fields

• DOI: 10.1214/19-aap1511
• 发表时间: 2020-04
• 期刊: The Annals of Applied Probability
• 作者: S. Ankirchner;A. Fromm;T. Kruse;A. Popier

Optimal Control of Diffusion Coefficients via Decoupling Fields

通过解耦场优化扩散系数控制

• DOI: 10.1137/17m1152401
• 发表时间: 2018
• 期刊: SIAM J. Control. Optim.
• 作者: Stefan Ankirchner;Alexander Fromm
• 通讯作者: Alexander Fromm